Algebra Nation Glossary of Terms (Geometry) - English Version · 2019-08-20 · Algebra Nation Glossary of Terms Vocabulary Word Definition Example AlgebraNation.com 1 Adjacent angles

Algebra Nation Glossary of Terms

Vocabulary Word Definition Example

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Adjacent angles Because these angles pairs share a ray, they are called adjacent angles.

Alternate exterior angles

Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on

opposite sides of the transversal.



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Alternate exterior angles theorem

If two parallel lines are cut by a transversal., the alternate exterior angels are congruent.

Alternate interior angles

Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on

opposite sides of the transversal.

Alternate interior angles theorem

If two parallel lines are cut by a transversal, the alternate interior angles are congruent.



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Angle An angle is formed by two rays with the same endpoint.

Angle bisector A line that splits an angle into two equal angles.

Angle pair Angle pairs share a ray.



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Angle-angle similarity(AA ~)

Criterion

If two angles of one triangle are congruent to two angles of another triangle, then the two

triangles are similar.

Angle-angle-side (AAS)

congruence postulate

If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of a second triangle, then the two

triangles are congruent.

Angle-preserving transformation All angles keep the same measure



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Angle-side-angle (ASA)


If two angles and the included side of one triangle are congruent to two angles and the

included side of a second triangle, then the two triangles are congruent.

Arc An arc is a section of the circumference of a circle, or any curve.

Base angle theorem and its

converse

The base angle theorem states that if two sides in a triangle are congruent, then the angles

opposite to these sided are also congruent. The converse of this theorem is also true. If two angles

of a triangle are congruent, then the sides opposite to these angels are congruent.



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Bisector A bisector divides lines, angles, and shapes into two equal parts.

Cavalieri’s Principle

Cavalieri’s principle is a strategy that can be used for approximating the area and volume of an irregular shaped figure. To use the Cavalieri’s Principle, we divide a figure into familiar shapes

to determine the total area or volume of the original shape.

Center The center of a polygon is the point equidistant from every vertex.



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Center of dilation The center of dilation is a fixed point in the plane

about which all points are expanded or contracted.

Central angle The central angle of a polygon is the angle made

at the center of the polygon by any two adjacent vertices of the polygon.

Chords distance to center theorem

In congruent circles or the same circle, chords are congruent if and only if they are equidistant

from the center.

Circumference The perimeter of the circle is known as the circumference.

The circumference can be calculated by using the equation 𝐶 = 2𝜋𝑟.



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Circumscribed angle

A circumscribed angle is an angle with rays tangent to the circle. It is equal to half of the

difference between the intercepted arcs.

Circumscribed circle

A circumscribed circle is the circle drawn on the outside that contains a given triangle.

Complementary angles

Two positive angles that together form a right angle are called complementary angles.



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Composition of isometries Composition of transformations (rigid)

Composition of transformations Putting two or more transformations together Musical piece, footprints, balloon filled with air being

let go

Cone

A cone is a solid geometric figure that has a flat base (that is frequently, though not necessarily, a circle) that tapers to a point called the apex or

vertex.

Congruent complements

theorem

If ∠𝐴 and ∠𝐵 are complements of the same angle, then ∠𝐴 and ∠𝐵 are congruent.



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Congruent supplements

theorem

If ∠𝐴 and ∠𝐵 are supplements of the same angle, then ∠𝐴 and ∠𝐵 are congruent.

Conjecture When you make a conjecture, you make an educated guess based on what you know or

observe.

If we look at data over the precipitation in a city for 29 out of 30 days and see that it has been raining

every single day it would be a good guess that it will be raining the 30th day as well.

Consecutive angles

Consecutive angles of a quadrilateral are angles with vertices that are consecutive.

Consecutive sides

Consecutive sides or adjacent sides of a quadrilateral are sides that have a common

endpoint.

𝐵𝐶, 𝐶𝐷𝐷𝐴, 𝐴𝐵𝐶𝐷, 𝐷𝐴𝐴𝐵, 𝐵𝐶




Consecutive vertices

Consecutive vertices or adjacent vertices of a quadrilateral are vertices that have endpoints of

the same side.

𝐵, 𝐴𝐴, 𝐷𝐵, 𝐶𝐷, 𝐶

Converse of the alternative

exterior angles theorem

If two lines are cut by a transversal and the alternate exterior angles are congruent, the lines

are parallel.

Converse of the alternative

interior angles theorem

If two lines are cut by a transversal and the alternate interior angles are congruent, the lines

are parallel.




Converse of the corresponding

angles theorem

If two lines are cut by a transversal and the corresponding angels are congruent, the lines

are parallel.

Converse of the hinge theorem

If two sides of one triangle are congruent to two sides of another triangle, and the third side of the

first triangle is greater than the third side of the second triangle, then the included angle of the first triangle is large than the included angle of

the second.

Converse of the same-side

consecutive angles theorem

If two lines are cut by a transversal and the interior angles on the same side of the transversal

are supplementary, the lines are parallel.




Converse Pythagorean

theorem

If the square of one side of a triangle is equal to the sum of the squares of the other two sides,

then the triangle is a right triangle.

Is a triangle with the lengths 20, 21, and 29 a right triangle?

20. + 21. = 29.

Corresponding angles

Any pair of angles each of which is on the same side of one of two lines cut by a transversal and

on the same side of the transversal.

Corresponding angles theorem

If two parallel lines are cut by a transversal, the corresponding angles are congruent.




CPCTC Corresponding parts of congruent triangles are congruent.

Cross section A cross section is the shape we get when cutting straight through a solid with a plane.

Cyclic quadrilateral

In a cyclic quadrilateral every vertex is on the circumference of a circle, and the opposite

angles of the quadrilateral are supplementary.




Cylinder

A cylinder is a solid geometric figure with two parallel and congruent circular bases and

circular or oval cross sections that are congruent at the bases.

Degrees to radians

To convert from degrees to radians, multiply the angels by 2

345°.

160° ·

𝜋180

=160𝜋180

=89𝜋

Diagonal A diagonal of a quadrilateral is a line segment

with endpoints that are two nonadjacent vertices of the quadrilateral.

Diagonals

A polygon’s diagonals are line segments from one vertex to another nonconsecutive vertex.

The number of diagonals of an n-sided polygon is :(:<=)

..




Dilation A dilation changes the size of an object through an enlargement or a reduction.

Distance Distance is an amount of space (in certain units) between two points on a plane.

Distance formula

The distance formula is used to determine the distance, d, between two points.

The distance formula is derived by creating a triangle and using the Pythagorean theorem to

find the length of the hypotenuse.

(𝑥. − 𝑥3). + (𝑦. − 𝑦3).




Double reflections Reflect twice (over both axes)

Exterior angles of a polygon

An exterior angle of a polygon I an angle that forms a linear pair with one of the interior angles

of the polygon.

General form of

a circle General form always has 𝑥.+𝑦. as its first two

terms 𝑎𝑥. + 𝑏𝑦. + 𝑐𝑥 + 𝑑𝑦 + 𝑒 = 0 where 𝑐, 𝑑, 𝑒 are constants




Geometric constructions Designing with tools

Straightedge compass

Geometric mean theorem: altitude

rule

In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the geometric mean of the lengths of the two

segments.

Geometric mean theorem: leg rule

In a right triangle, the amplitude from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of each leg of the

right triangle is the geometric mean of the lengths of the hypotenuse and the segment of

the hypotenuse that is adjacent to the leg.

Geometry

Geometry means “earth measurement,” and it involves the properties of points, lines, planes,

and figures.

Visual, spatial branch of math concerned with measurements of length, area, volume, perimeters, circumference, etc.




Glide reflections Reflect and shift

Hinge theorem

If two sides of one triangle are congruent to two sides of another triangle, and the included angles

are not congruent, then the longer third side is opposite the larger included angle.

Hypotenuse-leg (HL)theorem

Two right triangles are said to be congruent if their corresponding hypotenuse and at least one

of their legs are congruent.




Inscribed angles conjectures

In a circle, the measure of an inscribed angle is half the measure of the central angle with the

same intercepted arc. In a circle, two inscribed angles with the same intercepted arc are

congruent. Any angle inscribed in a semi-circle is a right angle.

Inscribed circle An inscribed circle will touch each of the three sides of the triangle at exactly one point.




Interior angles of a polygon

Interior angles of a polygon are the angles on the inside of the polygon formed by each pair of

adjacent sides.

Intersecting chords theorem

If two chords intersect on the interior of a circle, then the product of the lengths of the segments

of one chord is equal to the product of the lengths of the segments of the other chord.

𝐵𝑇 · 𝐴𝑇 = 𝑆𝑇 · 𝐸𝑇

Irregular polygons

Irregular polygons do not have congruent sides and angles.




Lateral face Each base edge and apex form a triangle

Line A line is a straight path that continues in both directions forever. Lines are one-dimensional.

Line segment A line segment is a portion of a line located between two points.

Linear pair The angles form a straight angle.




Linear pair postulate

If two positive angles form a linear pair, then they are supplementary.

Median The median of a trapezoid is another term for the midsegment.

Midpoint A point on a line segment that divides it into two equal parts.

Midsegment theorem for trapezoid

The midsegment of a trapezoid is parallel to each base and its length is one half the sum of the

lengths of the bases.




Net A net is a composition of two-dimensional faces that is formed by unfolding a three-dimensional

figure.

Non-rigid A non-rigid transformation changes the size of the pre-image. dilation

Opposite angles Opposite angles of a quadrilateral are angles with vertices that are not consecutive.

∠𝐵, ∠𝐷 ∠𝐴, ∠𝐶

Opposite sides Opposite sides of a quadrilateral are sides that do not have a common endpoint.

𝐵𝐶, 𝐴𝐷 𝐴𝐵, 𝐷𝐶




Parallel lines Parallel lines are two lines on the same plane that do not intersect.

Parallelogram

A parallelogram is a quadrilateral in which two pairs of opposite sides are parallel and

congruent, and two pairs of opposite angles are congruent.

Parallelogram theorem

A diagonal divides a parallelogram into two congruent triangles. Two consecutive angles of a parallelogram are supplementary. The diagonals

of a parallelogram bisect each other.

Partition A division into or distribution in portions or shares.




Perpendicular bisector

The perpendicular bisector is a line that divides a line segment into two equal parts. It also makes a right angle with the line segment. Each point on the perpendicular bisector is the same distance from each of the endpoints of the original line

segment.

Perpendicular bisector theorem

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints

of a segment.

Perpendicular lines

Perpendicular lines are two intersecting lines that form a 90 ͦ angle.

𝐴𝐵 ⊥ 𝑀𝑁




Perpendicular to a chord theorem

If the diameter of a circle is perpendicular to a chord, then the diameter bisects the chord.

Perpendicular transversal theorem

In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other

line also.




Perpendicular transversal theorem corollary

If two lines are both perpendicular to a transversal, then the lines are parallel.

Plane A plane is a flat, two-dimensional object. It has no thickness and extend forever.

Plane rotations Rotating a polygon around a given line

Sphere cone cylinder




Point A point is a precise location or place on a plane. It is usually represented by a dot.

Postulate

A postulate is a statement that we take to be automatically true. We do not need to prove that

a postulate is true because it is something we assume to be true

Through any two points there is exactly on line.

Pre-figure A pre-figure or pre-image is the original object.




Prime notation The prime notation (‘) is used to represent a transformed figure of the original figure.

Prism A prism is a solid geometric figure with two

polygonal bases that are congruent and parallel, with sides that are parallelograms.

Protractor We often use a protractor to measure angles.




Protractor postulate

The measure of an angle is the absolute value of the difference of the real numbers paired with

the sides of the angel, because the parts of angles formed by rays between the sides of a

linear pair add to the whole, 180 ͦ.

Pyramid A pyramid is a solid formed by connecting a polygonal base and a point, called the apex.

Pythagorean theorem

In a right triangle, the square of the hypotenuse (the side opposite to the right angle) is equal to

the sum of the squares of the other two sides.

𝑎. + 𝑏. = 𝑐.




Quadrilateral A quadrilateral is a polygon with four sides.

Radians Radians is the number of times the radius goes around a circle. 𝑅𝑎𝑑𝑖𝑎𝑛𝑠 = QRSQTUVWSW:QW

SXYRTZ= .2S

S= 2𝜋

Radians to degrees

To convert radians to degrees, multiply the angle by 345°

2.

11𝜋6

·180°𝜋

=180°(11)

6= 30° 11 = 330°

Radius The radius is the size of the circle and determines the arc length.

Ratio A ratio compares two numbers. A 1:1 ratio is stated as, or can also be written as, “1 to 1”.

Ray A ray is a piece of a line that starts at one point and extends infinitely in one direction.




Reflection A reflection flips the object over a line (as in mirror image).

Regular polygons Regular polygons have congruent sides and angles.




Right angles theorem All right angles are congruent.

Right triangle altitude theorem

If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.

Rigid A rigid transformation does not change the size of the pre-image. Translation, reflection, rotation

Rotation A rotation turns the shape around the center point.




Same-side consecutive

angles theorem

If two parallel lines are cut by a transversal, the interior angles on the same side of the transversal

are supplementary.

Scale factor The scale factor refers to how much the figure grows or shrinks, and is denoted by 𝑘.

If 0 < 𝑘 < 1, the image gets smaller and closer to the center of dilation.

If 𝑘 > 1, the image gets larger and farther from the center of dilation.

Secant A secant is a line that intersects a circle at two points.

Sector A sector is a region bounded by two radii of a circle and their intercepted arc.




Segment addition postulate

If three points, 𝐴, 𝐵, and 𝐶, are collinear and 𝐵 is between 𝐴 and 𝐶, then 𝐴𝐵 + 𝐵𝐶 = 𝐴𝐶.

𝐴𝐶 + 𝐶𝐷 = 𝐴𝐷

Segment bisector A segment bisector is a line, segment, or ray that passes through another segment and cuts it into

two congruent parts.




Side-Side-Side (SSS~)Criterion

If the lengths of the corresponding sides of two triangles are proportional, then the triangles are

similar.

Side-angle-side (SAS)


If two sides and the included angle of one triangle are congruent to two sides and the

included angle of a second triangle, then the two triangles are congruent.

Side-angle-side similarity

(SAS~)criterion

If the lengths of two sides are proportional and their included angles are congruent on two

different triangles, then the triangles are similar.




Side-side-side (SSS)


If three sides of one triangle are congruent to three sides of a second triangle, then the two

triangles are congruent.

Sphere A sphere is a set of points in 3D space equidistant from a point called the center of the sphere.

Standard form The standard form for the equation of a circle has a center (ℎ, 𝑘) and radius 𝑟. (𝑥 − ℎ).+(𝑦 − 𝑘). = 𝑟.

Supplementary angles

Two positive angles that form a straight line together are called supplementary angles. When added together, the measures of these angles is

180 degrees, forming a linear pair.




Tangent A tangent is a line in the plane of a circle that intersects the circle at exactly one point.

Tangent chord angle theorem

The measure of an angle formed by a chord and a tangent line is half the measure of the

intercepted arc.

Tangent segments theorem

If two segments are tangents to a circle from the same exterior point, they are congruent.




Tangent theorem

If a line is tangent to a circle, then the line is perpendicular to the radius at the point of tangency. The converse is also true: If a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle.

Theorems about kites

If a quadrilateral is a kite: Its diagonals are perpendicular. It has one pair of congruent

opposite angles. One of its diagonal forms two congruent triangles. It has one diagonal that bisects a pair of opposite angles. It has one

diagonal that bisects the other diagonal. If one of the diagonals of a quadrilateral is the perpendicular bisector of the other, the

quadrilateral is a kite.

Theorems about rectangles

All angles of a rectangle are right angles. The diagonals of a rectangle are congruent. If a

quadrilateral is equiangular, then it’s a diagonal. If the diagonals of a parallelogram are

congruent, the parallelogram is a rectangle.




Theorems about squares and

rhombi

A rhombus is an equilateral quadrilateral. A square is a rhombus and a rectangle. If one of

the angles of a rhombus is a right angle, then the rhombus is a square.

Theorems about the rhombus

All sides of a rhombus are congruent. The diagonals of a rhombus are perpendicular to

each other. The diagonals of a rhombus bisect its angles. If a quadrilateral is equilateral, then it is a rhombus. If the diagonals of a parallelogram are

perpendicular to each other, the parallelogram is a rhombus.

Theorems about trapezoids

If a quadrilateral is an isosceles trapezoid, its pairs of base angles is congruent. Its diagonals are

congruent.




Transformations Movements of objects on a coordinate plane

Translation A translation slides the shape in any direction.




Triangle inequality theorem

The sum of the lengths of any two sides of a triangle is greater that the length of the third side.

𝐴𝐵 + 𝐵𝐶 > 𝐴𝐶, 𝐵𝐶 + 𝐴𝐶 > 𝐴𝐵, 𝐴𝐶 + 𝐴𝐵 > 𝐵𝐶

Triangle midsegment

theorem

The midsegment of a triangle joins the midpoints of two sides of a triangle such that it length is half the length of the third side of the triangle and it is

parallel to the third side of the triangle.

Triangle sum theorem The sum of the interior angles in a triangle is 180°.

𝑚∠𝐴 +𝑚∠𝐵 +𝑚∠𝑐 = 180°




Vertex The point where the rays meet is called the vertex.

Vertical angles Vertical angles are opposite angles.

Vertical angles theorem

If two angles are vertical angles, then they have the same measure.

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Algebra Nation Glossary of Terms (Geometry) - English Version · 2019-08-20 · Algebra Nation Glossary of Terms Vocabulary Word Definition Example AlgebraNation.com 1 Adjacent angles